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Published in:
2018 | OriginalPaper | Chapter
8. Associated Processes
Author : Paul Doukhan
Published in: Stochastic Models for Time Series
Publisher: Springer International Publishing
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Abstract
The notion of association, or positive correlation, was naturally introduced in two different fields: reliability (Esary, Proschan, Walkup in Annal Math Stat 38:1466–1474, 1967) and statistical physics (Fortuin, Kasteleyn, Ginibre in Commun Math Phys 22–2:89–103, 1971) to model a tendency that the coordinates of a vector valued random variable admit such behaviours. We refer the reader to Newman (Inequalities in Statistics and Probability, Elsevier, Amsterdam, pp. 127–140, 1984) for more details. This notion deserves much attention since it provides a class of random variables for which independence and orthogonality coincide. Another case for which this feature holds is the Gaussian case, see Chap. 5. The notion of independence is more related to \(\sigma \)-algebras but in those two cases it is related to the geometric notion of orthogonality. Those remarks are of interest for modelling dependence as this is the aim of Chap. 9.